6.1 Ratios And Unit Rates


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Chapter 6, Section 1: Ratios and Unit Rates

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6.1 Ratios And Unit Rates

  1. 1. Warm Up: 30/8 (  decimal) 1.07 (  Fraction) 3/7t = 3/8 (  Solve)
  2. 2. Chapter 6: Ratios, Proportions, and Percents And you thought fractions where a pain. Section 1: Ratios and Unit Rates
  3. 3. Example <ul><li>In 2001, about 10 out of every 15 people eligible to vote were registered to vote. </li></ul>10 out of 15 is a ratio. Express it as a Fraction and Simplify. There are multiple ways to write this ratio: 10 : 15, 10 to 15, and 10/15
  4. 4. Finding Ratios In Words <ul><li>Students were asked in a survey whether they had after-school jobs. Write each ration as a fraction in simplest form. </li></ul>Find the ratio of Students With Jobs compared to Students Without Jobs. Find the ratio of Students Without Jobs compared to All of the Students Surveyed. 100 Total 60 Don’t Have a Job 40 Have a Job Number Response
  5. 5. Write Each Ratio As a Fraction In Simplest Form. <ul><li>a) Students with jobs to students surveyed. </li></ul><ul><li>b) Students without jobs to students with jobs. </li></ul><ul><li>Hint: The first number </li></ul><ul><li>mentioned goes first, the </li></ul><ul><li>second number mentioned </li></ul><ul><li>goes second. </li></ul>100 Total 60 Don’t Have a Job 40 Have a Job Number Response
  6. 6. Definition <ul><li>Ratio: a comparison of two quantities by division. </li></ul><ul><li>This is why you can write ratios as fractions (and why Ratio nal Numbers are numbers that can be written as Fractions). </li></ul><ul><li>So, A to B, A : B, or A/B. </li></ul>
  7. 7. When Comparing, Rates Are Necessary. <ul><li>A Rate is a Ratio that Compares Quantities in Different Units. </li></ul><ul><li>A UNIT RATE is a rate that has a DENOMINATOR of 1. </li></ul><ul><li>Use this at the Grocery Store to find the Best Price on Purchases. </li></ul><ul><li>$2.17/1 gallon (like gas prices a week ago) </li></ul><ul><li>$3.50/1 pound (most meat these days) </li></ul>
  8. 8. Real Life Example <ul><li>Which size of dish soap has the lowest unit price? (Lowest Price Per Ounce) </li></ul><ul><li>Convert size into a ratio, Price:Volume. </li></ul>Mini: $1.20/12 = $0.10/1 fl oz Family: $2.24/28 = $0.08/1 fl oz Economy: $3.60/40 = $0.09/1 fl oz This is a unit price. For every one ounce, that’s how much you pay for it. $3.60 40 Economy $2.24 28 Family $1.20 12 Mini Price Volume (fl oz) Size
  9. 9. What is the Price of 1: Unit Price <ul><li>Two liters of spring water costs $1.98. </li></ul><ul><li>$1.98/2 liters </li></ul><ul><li>Divide $1.98/2 liters  price of 1 liter. </li></ul><ul><li>$0.98/1 liter = Unit Price </li></ul><ul><li>A car goes 425 miles on 12.5 gallons of gas. </li></ul><ul><li>425miles/12.5 gallons </li></ul><ul><li>Divide 425miles/12.5 gallons  miles in 1 gallon of gas. </li></ul><ul><li>34 miles/1 gallon = Unit Mileage </li></ul>
  10. 10. Dimensional Analysis <ul><li>Use Dimensional Analysis to choose Conversion Factors for Converting Rates and Ratios. </li></ul><ul><li>Convert 10 miles/hour to feet/minute. </li></ul>10 miles hour = 10 miles hour 5,280 feet 1 mile X X 1 hour 60 minutes Cross Reduce! 880 feet minute
  11. 11. Try These For Me: Convert <ul><li>3.5 quart/minute = ___ gallon/hour </li></ul><ul><li>12 centimeter/second = ___ meter/hour </li></ul>
  12. 12. Talk It Out and Give Me Examples <ul><li>A student claims that a ratio remains unchanged if 1 is added to both the numerator and the denominator of the fraction. Does a/b equal a+1/b+1? </li></ul>
  13. 13. One More Problem <ul><li>Density is the ratio of a substance’s mass to its volume. A volume of 20 cubic centimeters of gold has a mass of 386 grams. Express the density of gold as a unit rate. </li></ul>19.3 gram/centimeter cubed
  14. 14. Assignment #42 <ul><li>Page 280 : 12-35 All , 38. </li></ul><ul><li>MAKE SURE YOU WRITE THIS DOWN CORRECTLY!!! </li></ul>